Conditional Simulation of Stationary Non-Gaussian Processes Based on Spectral Representation and Unified Hermite Polynomial Model: Application to Reconstruction of Missing Measurement Data

Conditional stochastic processes simulation is an effective approach for reconstructing missing data in monitoring systems, which plays a crucial role in engineering disaster prevention and mitigation. This paper proposes a conditional non-Gaussian stochastic process simulation method. The method first establishes a conversion mapping between non-Gaussian and underlying Gaussian processes using the Unified Hermite Polynomial Model (UHPM). It then constructs the cross-spectrum matrix based on the actual Gaussian auto-spectrums of the recorded samples and the Gaussian auto-spectrums of the target samples. Using the Spectral Representation Method (SRM), random Fourier coefficients are conditionally generated to simulate the Gaussian samples at the target points, which are subsequently mapped into non-Gaussian samples via the UHPM. The effectiveness and accuracy of the proposed method are validated through simulations based on fluctuating wind pressure coefficients and measured fluctuating wind speeds.